is the plane containing
'ough S and v.
its normal vector n be
S Yvi-Ys -Zs
L Yk —YL 0
(30
a
Yi —YL) (51)
(Xk — XL)
X 7 has the form:
Yk)+1Z =0 (32)
of the normal vector n
+ mt
+ nt (33)
+ It
nto(32) yields the val-
corresponding to the
; coordinates will be:
+ mt
+ nt (34)
TOP
= SP’ and the angle
found to be:
1? + 02d,
l
se
OF SPACE MOD-
t of intersection of the
ecting each station po-
int. After determining
|, camera and the space
ations(S;, S,) for both
(8)), the space coordi-
of two corresponding
OW:
whose image is A. ( in
neous coordinates can
equation(3). Then the
alculated as mentioned
Space coordinates for
; A; (in left photo) can
enna 1996
S
x
Si Right photo
Lett photo
Figure 8: Space intersection with a stereopair of pho-
tos
2. The space point A can be easily found as the
point of intersection of two rays S; Aa, and
Sr Aa
re
These steps depend only on knowing the coordinates
of both S; and S,. Hence for the reconstrection of
the space model the orientation parameters need not
be all calculated.
However, due to errors in measurement, the two cor-
responding rays are skew in general. Therefore, the
shortest distance between them is calculated and the
space point A is assumed to be the midpoint of it.
5. COMPUTER PROGRAMS
A computer program was developed using the pro-
posed method. The program takes also into consid-
eration the case of giving more than four coplanar
points and/ or more than one control points outside,
using the least squares technique.
Another computer program relying on the same idea
is developed to deal with the reconstruction of a space
model, using two images form two different positions
using the same camera, without calculating the ori-
entation parameters.
6. ACCURACY
For the estimation of the accuracy of the method the
Standard deviation for the coordinates of a group of
check points (with known space and image coordi-
nates) were calculated.
The test was done with a mathematical simulation of
a photo of an object consisting of 30 points (6 points
as control points) and the rest as check points [2].
1. The orientation parameters of the camera were
regarded as known for right and left photos and
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996
were used to calculate the image coordinates
X,Y of the points.
2. A random numbers were added to each photo
coordinates (0 — — + 0.05mm) to simulate the
measuring errors and random deformation.
3. The orientation parameters were recalculated
from new photo coordinates of the control po-
sition which were used to determine the space
coordinates of the check points.
4. Standard deviation in X,Y and Z direction can
be determined by finding the difference between
the original, initially given coordinates and the
corresponding calculated one [3].
The following Table shows the standard deviation
Ox,0y,07 and oxyz for check points calculated by
the proposed method.
| St. dev.(in em) | ex | ev | ez | oxvz |
| Proposed method | 0.17 | 0.18 | 0.42 | 0.487 |
7. CONCLUSION
The proposed method is used to determine the ori-
entation parameters of a non-metric camera and also
can be used to find the exterior parameters of a met-
ric camera. The main advantage of this method is
that the orientation parameters are determined di-
rectly without using linearization of equations and
they need no complicated technique.
A practical use of this method is when photos of ob-
jects contain plane figures such as buildings, interior
furniture, ... etc. Old non-metric photos can also be
interpreted and photogrammetric measurements can
be taken to such objects.
References
[1] ELsoNBATY A. M.,1992. Using Perspective Pro-
jection For Estimating The Accuracy Of Mea-
surements in Photogrammetry. MSC Thesis,
Civil Eng. Dept. Assiut University.
ETHROG, U.,1984. Non-metric Camera Calibra-
tion and Photo Orientation Using Parallel and
Perpendicular lines of the Photographed Object,
Photogrammetria 39, pp. 13-22
[2
—
[3] MIKHaIL E. H., GRACIES G.,1981. Analysis and
Adjustment of Survey Measurements, Litton Ed-
ucational Publishing.
(4] WILLIAMsoN J. R., BRILL M. H.,1987. Three-
dimensional Reconstruction From two-Point
Perspective Imagery, Photogrammetric Eng. and
Remote Sensing, 53 pp. 331-335.
